Continuity Scaling: A Rigorous Framework for Detecting and Quantifying Causality Accurately

Xiong, Ying; Leng, Siyang; Ma, Huanfei; Nie, Qing; Lai, Ying Cheng; Lin, Wei

doi:10.34133/2022/9870149

Cited by 20 publications

(15 citation statements)

References 60 publications

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“…Furthermore, AC-PCoA can be used as a preprocessing step before applying other machine learning methods, such as regression and clustering. Since more and more biological data are used for diagnostic, predictive and classification applications nowadays, it is of paramount importance that AC-PCoA as well as its idea can be further generalized to such scenarios, and even causality analytics [ 40 , 41 ].…”

Section: Discussionmentioning

confidence: 99%

AC-PCoA: Adjustment for confounding factors using principal coordinate analysis

et al. 2022

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Confounding factors exist widely in various biological data owing to technical variations, population structures and experimental conditions. Such factors may mask the true signals and lead to spurious associations in the respective biological data, making it necessary to adjust confounding factors accordingly. However, existing confounder correction methods were mainly developed based on the original data or the pairwise Euclidean distance, either one of which is inadequate for analyzing different types of data, such as sequencing data. In this work, we proposed a method called Adjustment for Confounding factors using Principal Coordinate Analysis, or AC-PCoA, which reduces data dimension and extracts the information from different distance measures using principal coordinate analysis, and adjusts confounding factors across multiple datasets by minimizing the associations between lower-dimensional representations and confounding variables. Application of the proposed method was further extended to classification and prediction. We demonstrated the efficacy of AC-PCoA on three simulated datasets and five real datasets. Compared to the existing methods, AC-PCoA shows better results in visualization, statistical testing, clustering, and classification.

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Section: Discussionmentioning

confidence: 99%

AC-PCoA: Adjustment for confounding factors using principal coordinate analysis

et al. 2022

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“…However, the study of the transition to the stationary process or even the non-stationary processes, though rather difficult, could be the potential direction. Indeed, data-driven methods (Hou et al, 2022;Ying et al, 2022) could be the potential tools for studying these transition processes.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Complex Dynamics of Noise-Perturbed Excitatory-Inhibitory Neural Networks With Intra-Correlative and Inter-Independent Connections

Peng

Lin

2022

Front. Physiol.

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Real neural system usually contains two types of neurons, i.e., excitatory neurons and inhibitory ones. Analytical and numerical interpretation of dynamics induced by different types of interactions among the neurons of two types is beneficial to understanding those physiological functions of the brain. Here, we articulate a model of noise-perturbed random neural networks containing both excitatory and inhibitory (E&I) populations. Particularly, both intra-correlatively and inter-independently connected neurons in two populations are taken into account, which is different from the most existing E&I models only considering the independently-connected neurons. By employing the typical mean-field theory, we obtain an equivalent system of two dimensions with an input of stationary Gaussian process. Investigating the stationary autocorrelation functions along the obtained system, we analytically find the parameters’ conditions under which the synchronized behaviors between the two populations are sufficiently emergent. Taking the maximal Lyapunov exponent as an index, we also find different critical values of the coupling strength coefficients for the chaotic excitatory neurons and for the chaotic inhibitory ones. Interestingly, we reveal that the noise is able to suppress chaotic dynamics of the random neural networks having neurons in two populations, while an appropriate amount of correlation coefficient in intra-coupling strengths can enhance chaos occurrence. Finally, we also detect a previously-reported phenomenon where the parameters region corresponds to neither linearly stable nor chaotic dynamics; however, the size of the region area crucially depends on the populations’ parameters.

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“…xt ðÁÞ performs the inverse operation. What was proposed in [32] means that if causality exists, there is a continuous map between the two spaces (L y and L x ). Thus, if we consider a neighbourhood in L x of radius e x that maps to the space L y using inverse function fÀ1…”

Section: Continuity Scaling Methodsmentioning

confidence: 99%

“…Similarly, f^xt−1false(⋅false) performs the inverse operation. What was proposed in [32] means that if causality exists, there is a continuous map between the two spaces (scriptLy and scriptLx). Thus, if we consider a neighbourhood in scriptLx of radius ϵx that maps to the space scriptLy using inverse function f^xt−1false(⋅false), we should obtain a neighbourhood in scriptLy whose radius δ y must be an increasing function of ϵx.…”

Section: Causality Detection Methodsmentioning

confidence: 99%

“…Accordingly, the main objectives of this study are: (i) to determine the conditions under which CS [32] and CCS [29] methods can be safely applied to detect causality in real-world time series, (ii) to highlight the advantages and limitations of both methods for scientists within the Ecology, Biology, Earth and Marine Science communities, among others, who can use these methods to detect causal networks.…”

Section: Introductionmentioning

confidence: 99%

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Usefulness and limitations of convergent cross sorting and continuity scaling methods for their application in simulated and real-world time series

2023

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Causality detection methods are valuable tools for detecting causal links in complex systems. The efficiency of continuity scaling (CS) and the convergent cross sorting (CSS) methods to detect causality was analysed. Usefulness and limitations of both methods in their application to simulated and real-world time series was explored under different scenarios. We find that CS is more robust and efficient than the CSS method for all simulated systems, even when increasing noise levels were considered. Both methods were not able to infer causality when time series with a marked difference in their main frequencies were analysed. Minimum time-series length required for the detection of a causal link depends on intrinsic system dynamics and on the method selected to detect it. Using simulated time series, only the CS method was capable to detect bidirectional causality. Causality detection, using the CS method, should at least include: (i) causality strength convergence analysis, (ii) statistical tests of significance, (iii) time-series standardization, and (iv) causality strength ratios as a strength indicator of relative causality between systems. Causality cannot be detected by either method in simulated time series that exhibit generalized synchronization.

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Continuity Scaling: A Rigorous Framework for Detecting and Quantifying Causality Accurately

Cited by 20 publications

References 60 publications

AC-PCoA: Adjustment for confounding factors using principal coordinate analysis

AC-PCoA: Adjustment for confounding factors using principal coordinate analysis

Complex Dynamics of Noise-Perturbed Excitatory-Inhibitory Neural Networks With Intra-Correlative and Inter-Independent Connections

Usefulness and limitations of convergent cross sorting and continuity scaling methods for their application in simulated and real-world time series

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